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- Use the slope–intercept form of
The equation
models the relation between the amount of Tuyet’s monthly water bill payment,
P , in dollars, and the number of units of water,
w , used.
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ⓐ Find Tuyet’s payment for a month when 0 units of water are used.
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ⓑ Find Tuyet’s payment for a month when 12 units of water are used.
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ⓒ Interpret the slope and
P -intercept of the equation.
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ⓓ Graph the equation.
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The equation
models the relation between the amount of Randy’s monthly water bill payment,
P , in dollars, and the number of units of water,
w , used.
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ⓐ Find the payment for a month when Randy used 0 units of water.
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ⓑ Find the payment for a month when Randy used 15 units of water.
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ⓒ Interpret the slope and
P -intercept of the equation.
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ⓓ Graph the equation.
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ⓐ $28
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ⓑ $66.10
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ⓒ The slope, 2.54, means that Randy’s payment,
P , increases by $2.54 when the number of units of water he used,
w, increases by 1. The
P –intercept means that if the number units of water Randy used was 0, the payment would be $28.
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ⓓ
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Bruce drives his car for his job. The equation
models the relation between the amount in dollars,
R , that he is reimbursed and the number of miles,
m , he drives in one day.
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ⓐ Find the amount Bruce is reimbursed on a day when he drives 0 miles.
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ⓑ Find the amount Bruce is reimbursed on a day when he drives 220 miles.
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ⓒ Interpret the slope and
R -intercept of the equation.
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ⓓ Graph the equation.
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Janelle is planning to rent a car while on vacation. The equation
models the relation between the cost in dollars,
C , per day and the number of miles,
m , she drives in one day.
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ⓐ Find the cost if Janelle drives the car 0 miles one day.
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ⓑ Find the cost on a day when Janelle drives the car 400 miles.
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ⓒ Interpret the slope and
C –intercept of the equation.
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ⓓ Graph the equation.
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ⓐ $15
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ⓑ $143
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ⓒ The slope, 0.32, means that the cost,
C , increases by $0.32 when the number of miles driven,
m, increases by 1. The
C -intercept means that if Janelle drives 0 miles one day, the cost would be $15.
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ⓓ
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Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation
models the relation between her weekly salary,
S , in dollars and the amount of her sales,
c , in dollars.
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ⓐ Find Cherie’s salary for a week when her sales were 0.
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ⓑ Find Cherie’s salary for a week when her sales were 3600.
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ⓒ Interpret the slope and
S –intercept of the equation.
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ⓓ Graph the equation.
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Patel’s weekly salary includes a base pay plus commission on his sales. The equation
models the relation between his weekly salary,
S , in dollars and the amount of his sales,
c , in dollars.
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ⓐ Find Patel’s salary for a week when his sales were 0.
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ⓑ Find Patel’s salary for a week when his sales were 18,540.
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ⓒ Interpret the slope and
S -intercept of the equation.
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ⓓ Graph the equation.
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ⓐ $750
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ⓑ $2418.60
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ⓒ The slope, 0.09, means that Patel’s salary,
S , increases by $0.09 for every $1 increase in his sales. The
S -intercept means that when his sales are $0, his salary is $750.
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ⓓ
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Costa is planning a lunch banquet. The equation
models the relation between the cost in dollars,
C , of the banquet and the number of guests,
g .
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ⓐ Find the cost if the number of guests is 40.
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ⓑ Find the cost if the number of guests is 80.
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ⓒ Interpret the slope and
C -intercept of the equation.
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ⓓ Graph the equation.
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Margie is planning a dinner banquet. The equation
models the relation between the cost in dollars,
C of the banquet and the number of guests,
g .
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ⓐ Find the cost if the number of guests is 50.
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ⓑ Find the cost if the number of guests is 100.
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ⓒ Interpret the slope and
C –intercept of the equation.
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ⓓ Graph the equation.
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ⓐ $2850
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ⓑ $4950
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ⓒ The slope, 42, means that the cost,
C , increases by $42 for when the number of guests increases by 1. The
C -intercept means that when the number of guests is 0, the cost would be $750.
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ⓓ
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Use Slopes to Identify Parallel Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.
Use Slopes to Identify Perpendicular Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.
Everyday math
The equation
can be used to convert temperatures
F , on the Fahrenheit scale to temperatures,
C , on the Celsius scale.
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ⓐ Explain what the slope of the equation means.
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ⓑ Explain what the
C –intercept of the equation means.
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The equation
is used to estimate the number of cricket chirps,
n , in one minute based on the temperature in degrees Fahrenheit,
T .
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ⓐ Explain what the slope of the equation means.
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ⓑ Explain what the
n –intercept of the equation means. Is this a realistic situation?
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ⓐ For every increase of one degree Fahrenheit, the number of chirps increases by four.
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ⓑ There would be
chirps when the Fahrenheit temperature is
. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)
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Writing exercises
Self check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After looking at the checklist, do you think you are well-prepared for the next section? Why or why not?
Questions & Answers
If auger is pair are the roots of equation x2+5x-3=0
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
find product (-6m+6) ( 3m²+4m-3)
what is the solution
bill
how did you arrive at this answer?
bill
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
-6m(3mA²+4m-3)+6(3mA²+4m-3)
=-18m²A²-24m²+18m+18mA²+24m-18
Rearrange like items
-18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph.
1.x+2y=3
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
please why isn't that the 0is in ten thousand place
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
I am eliacin, I need your help in maths
Rood
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
how to reduced echelon form
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
d=r×t
the equation would be 8/r+24/r+4=3
worked out
Sheirtina
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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